The area under my kitchen cabinet houses my hot water supply. When the outside temp was close to 0, the hot water froze! Pipe didn't burst, but I'm concerned with further free zing it will. We tried leaving the door cabinet open, but the pipe is enclosed in the wall and apparently not well insulated. What's a quick way to get some heat against that wall so it won't freeze again??

Hot water freezes faster then cold, This is not the best option but when it is cold out let the water drip. Better insulation is the best idea but means pulling things apart. Best to do this in warmer weather.

I would open up the wall and at the very least the pipe would be heated more by the house air. While it's open you can check the insulation situation. If there is room place rigid insulation between the pipe and the outside wall. Hot water does not freeze faster than cold water. Chances are there isn't any insulation in the cavity or the pipe is against the outside wall.